Here we studied the effect of rare earth (Y) and transition metal (Co, Ni) substitution on the structure, magnetic and dielectric properties of the BiFeO3 (BFO) multiferroic ceramic. The samples were synthesized by modified rapid liquid phase sintering method. The phase purity and structural characteristics of the ceramics were investigated by X-ray diffraction and scanning electron microscope. The results revealed the uniform micro-structure with reduced grain size due to the rare earth doping in the BFO. Compared to the pure BFO, enhanced coercivity and resistivity were observed for the co-doped ceramics with Y and Co. The improvement of temperature stability of magnetism and electrical conductivity was found for ceramic co-doped with Y+3 and Ni+2 ions. The possible origin of the improvement in these properties has been discussed on the basis of the size effect and nature of the dopants.